Geodesic
Minimum supports of eigenfunctions with the second largest eigenvalue of the star graph
Vladislav Kabanov1 ; Elena V. Konstantinova2 ; Leonid Shalaginov3 ; Alexandr Valyuzhenich2
1Krasovskii Institute of Mathematics and Mechanics
2Sobolev Institute of Mathematics
3Chelyabinsk State University, Krasovskii Institute of Mathematics and Mechanics
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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The Star graph $S_n$, $n\ge 3$, is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(12),(13),\ldots,(1n)\}$. In this work we study eigenfunctions of $S_n$ corresponding to the second largest eigenvalue $n-2$. For $n\ge 8$ and $n=3$, we find the minimum cardinality of the support of an eigenfunction of $S_n$ corresponding to the second largest eigenvalue and obtain a characterization of eigenfunctions with the minimum cardinality of the support. A corrigendum was added November 19, 2020.
DOI : 10.37236/9147
Classification : 05C50, 05C25, 05E16, 05B30, 05C35
Mots-clés : spectrum of the star graph

Vladislav Kabanov  1   ; Elena V. Konstantinova  2   ; Leonid Shalaginov  3   ; Alexandr Valyuzhenich  2

1 Krasovskii Institute of Mathematics and Mechanics
2 Sobolev Institute of Mathematics
3 Chelyabinsk State University, Krasovskii Institute of Mathematics and Mechanics 
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     author = {Vladislav Kabanov and Elena V. Konstantinova and Leonid Shalaginov and Alexandr Valyuzhenich},
     title = {Minimum supports of eigenfunctions with the second largest eigenvalue of the star graph},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/9147},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/9147/}
}
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Vladislav Kabanov; Elena V. Konstantinova; Leonid Shalaginov; Alexandr Valyuzhenich. Minimum supports of eigenfunctions with the second largest eigenvalue of the star graph. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9147

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